A045900 Hypothetical numbers of terms in general expressions for coefficients of Lovelock Lagrangians.

1, 1, 3, 8, 25, 85, 318, 1234, 4884, 19458, 77727, 310761, 1242853, 4971151, 19884270, 79536639, 318145993, 1272583241, 5090332042, 20361326983, 81445306447, 325781223902, 1303124893253, 5212499570050, 20849998276525, 83399993101506, 333599972400353

Offset: 0

Author

C. C. Briggs (ccb104(AT)psu.edu)

Keywords

• nonn

Comments

Hypothetical extension of sequence A006372.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• C. C. Briggs, A General Expression for the Quintic Lovelock Tensor, arXiv:gr-qc/9607033, 1996-1997.
• C. C. Briggs, A General Expression for the Quartic Lovelock Tensor, arXiv:gr-qc/9703074, 1997.
• C. C. Briggs, Some Possible Features of General Expressions for Lovelock Tensors ..., arXiv:gr-qc/9808050, 1998-2000.

Crossrefs

Cf. A000041, A006372.

Programs

Mathematica

p = PartitionsP;
a[n_] := a[n] = If[n < 4, {1, 1, 3, 8}[[n+1]], a[n-3] - 3*a[n-2] + 3*a[n-1] - p[n-3] + 3*p[n-2] - 3*p[n-1] + p[n] + 2^(2*(n-3) + 1)];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 24 2019 *)

Formula

a(n+3) = 3*a(n+2) - 3*a(n+1) + a(n) + p(n+3) - 3*p(n+2) + 3*p(n+1) - p(n) + 2^(2*n + 1); a(n+4) = 7*a(n+3) - 15*a(n+2) + 13*a(n+1) - 4*a(n) + p(n+4) - 7*p(n+3) + 15*p(n+2) - 13*p(n+1) + 4*p(n); where p(n) is the partition function (i.e. number of partitions of n, A000041) and where p(0) = 1.

a(n) ~ 2^(2*n+1) / 27. - Vaclav Kotesovec, Jul 05 2025

Extensions

More terms from Jean-François Alcover, Feb 24 2019